Bates College SCARAB Honors Theses Capstone Projects Spring 5-2012 Objective Chances in a Deterministic World Daniel Lambright Bates College, dlambrig@bates.edu Follow this and additional works at: http://scarab.bates.edu/honorstheses Recommended Citation Lambright, Daniel, "Objective Chances in a Deterministic World" (2012). Honors Theses. 28. http://scarab.bates.edu/honorstheses/28 This Open Access is brought to you for free and open access by the Capstone Projects at SCARAB. It has been accepted for inclusion in Honors Theses by an authorized administrator of SCARAB. For more information, please contact batesscarab@bates.edu.
Bates College SCARAB Honors Theses 5-27-2012 Objective Chances in a Deterministic World Daniel Lambright This Restricted Access is brought to you for free and open access by SCARAB. It has been accepted for inclusion in Honors Theses by an authorized administrator of SCARAB. For more information, please contact mduvall@bates.edu.
Objective Chances in a Deterministic World An Honors Thesis Presented to The Faculty of the Department of Philosophy Bates College in partial fulfillment of the requirements for the Degree of Bachelor of Arts By Daniel Ross Lambright Lewiston, Maine 2012
ABSTRACT Determinism is the thesis that the state of the world at any time uniquely determines the state of the world at all future times. Our best scientific theories seem inconclusive as to whether our world is deterministic. Our world could very well be either partially or completely deterministic. But determinism is not as innocuous as it seems; the truth of determinism seems to come into conflict with many intuitive concepts. One such concept is objective chance. Our intuitive notions of objective chances are tied to the belief that events could have turned out differently than the way they actually occurred. Though many philosophers have declared that this conception of objective chance is incompatible with deterministic worlds, some have tried to provide accounts that render the two compatible. In this thesis I investigate what a theory of deterministic chance could be. Working within certain metaphysical constraints on chance, I craft out a new dispositional account of chance grounded in properties that objects have. ii
ACKNOWLEDGEMENTS My first philosophy course came in the first semester of my sophomore year. It was a 9:20 class on the philosophy of mind taught by Lauren Ashwell. Previous to Professor Ashwell s course I had no experience with metaphysics. The course started out roughly, not in the sense of comprehension of the ideas (which was certainly hard), but in finding a voice to say something of worth. Of course, the Kripkes, Putnams and Lewises of the world were not infallible but they sure as hell seemed like it. As I continued in my training my philosophical acumen increased. Not only was I getting better at thinking about metaphysics I was actually enjoying the challenging problems at its core. This is what motivated me to choose the topic of this thesis. I had no particular expertise on the topic before coming into the research; I had no personal connection to the topic and I had no push to take this as my topic. I merely saw a vexing metaphysical problem and wanted to intellectually challenge myself with issues I had not investigated in depth. This topic has certainly challenged me. From misunderstandings, to false starts and confusion I truly thank my advisor and first philosophy professor for her patience and good guidance. Her constructive critiques have been an integral part of forming my account and hopefully crafting a successful thesis. I would also like to thank the rest of the Philosophy department at Bates for their contributions to my intellectual development. Finally, my acknowledgments would not be complete without thanking my mother, father and friends for providing useful guidance in stressful times. iii
TABLE OF CONTENTS Introduction...1 Chapter 1...3 Section I..4 Section II...10 Section III..13 Chapter II.18 Section I.18 Section II 21 Section III..28 Section IV..34 Chapter III...39 Section 1 39 Section 2...44 Section 3 48 Section 4 50 Chapter IV...51 Section 1 51 Section 2 54 Section 3 58 Section 4 60 Chapter V.65 Section 1 65 Section 2 71 Section 3 75
INTRODUCTION What are we to make of seemingly conflicting concepts? Well, there are two possible courses of action: 1) argue that one of the concepts must be empty if the other concept is true or 2) argue that the seeming conflict does not exist. Philosophers who taken the first course of action are called incompatibilist of whatever concepts they are investigating, while philosophers attempting to show that two concepts to do not necessarily conflict are known as compatibilists. The most famous debate about compatibilism is the battle between hard determinist, libertarians, and compatibilists over free will. In fact the word compatibilism is mostly used to the position that the defenders of both determinism and free will. This thesis will address another type of compatibilism. The debate at the center of this thesis does not center directly on any notions of human agency but it does deal with determinism. The compatibilism at the heart of my thesis is the compatibilism between determinism and chance. Chances seem to creep into our lives at every junction. This is a chance your favorite football team with get the ball to start the game, your health insurance rate is in part a function of the chance of you getting ill, in Main there is often a chance of snow, and you might be given a certain chance of surviving cancer. We know that chances are related to probability and we even have the mathematical tools to calculate the chance of an event occurring but rarely do we think seriously about what chance really is. Like most concepts, the metaphysical depth of chance escapes our daily thought. This thesis will investigate what it means to be a chance and whether we could have chances in a deterministic world. My project will be a compatibilistic project that builds on existing metaphysical foundations. My intention is not to settle all of the issues that I use to build my account. It is impossible within the confines of this thesis to fully address the nuances of all 1
of the issues involved. What I do hope to do is provide a strong enough account of determinism and chance that can weather many different views on the smaller metaphysical foundations used to build the argument. The thesis is constructed on chapters that build on each other. The function of the first chapter is to work through the development of determinism to arrive at the working definition that is used in the remaining chapters of the thesis. The first chapter also functions to show the necessity of taking determinism seriously. In the second chapter I introduce the problem of deterministic chances in all of its glory. Chapters three and four are the chapters that lay the foundation for my positive account in chapter five. Chapter 3 introduces Antony Eagle s Can- Ability Principle (CAP)- a principle that I endorse because of its ability to show what would have to be true of an account of chance for it to posit deterministic chances. As I note in chapter three, CAP does not provide a full account of chance and so I turn, in chapter four, to evaluating Mellor s dispositional theory of chance. Finding Mellor s account promising yet flawed and incomplete, I seek to provide my own dispositional account of chance in the fifth and final chapter. 2
CHAPTER I CLIMBING UP THE TOWER Determinism is the perennial topic of philosophical discussion. Very little acquaintance with philosophical literature is needed to reveal the Tower of Babel character of the discussion: some take the message of determinism to [be] clear and straightforward while others find it vague and hopeless. Here we have, the cynic will say, a philosophical topic par excellence! 1 INTRODUCTION The history of philosophy is lined with debates that critically hinge on a notion of what determinism is or the truth of determinism. The most famous of these debates, of course, being on the compatibilism of free will and determinism. A less famous metaphysical debate involves the compatibility of determinism and chance. Though answers to both of these debates depend quite heavily on a conceptual definition of determinism, philosophers involved in these debates seem to rely on rather vague notions of the central concept. This phenomenon could be due to the an apparent simplicity of the concept or because the concept itself is inherently vague. John Earman points out this problem in the introduction to A Primer on Determinism. Earman s Primer is supposed to provide some conceptual clarity on both what determinism is and what it means to call something deterministic. Since my thesis is intimately linked to determinism I will follow Earman s lead in explicating a working definition of determinism that I will use for the remainder of this thesis. In this chapter I will work through the historical development of determinism to arrive at John Earman s formulation of Laplacean determinism. Using these insights, I will spell out what it would mean for the world to be deterministic. Specifically, I will 1 Earman (1986) p.1 3
briefly investigate the determinism or indeterminism of certain physical theories including classical mechanism and quantum mechanics. I. DEFINING DETERMINISM When we think about determinism we normally think of it in relation to events. If we think we live in a deterministic world, we think that, any event X is determined. Usually when we say something is determined we use it to mean that the outcome was already set and could not have occurred in any other way. Our intuitions on determinism can be teased out through a simple example using bouncing balls. If I drop a large amount of bouncing balls into a container, and our world is deterministic, then the balls actions will unfold in one and only one way. We also think that if we know all the laws and conditions affecting the balls behavior then we, in principle, should have epistemic access to every outcome of every bounce. a. Fatalism It is this intuition that scares the fans of human agency. It is thought that if determinism is true then our seeming human agency has no power to change and control the future. This intuition also becomes linked in our human mind with fatalism and destiny. One of the strongest pre-enlightenment connections between determinism and fatalism is seen in Greek civilization. In Greek mythology the Fates were goddesses who decided the course of an individual s life. Individuals were to merely follow their life s path and be subjected to the will of the Gods. Greek mythology is full of premonitions and oracles telling Greek heroes of their fate. The great Achilles knows he will die young but he also knows there is nothing that he can do to change this 4
predetermined fact. The link between fatalism and determinism is also seen in Wesley Salmon s retelling of a famous legend. the Stoic philosopher Epictetus, who was a slave, broke a vase that his master, who was a philosopher, treasured. When the master began to beat him, Epictetus protested, By the philosophy to which we both adhere, it was predestined from the beginning of the world that I should break the vase; I am not to blame and I should not be beaten. His master replied, By that same philosophy, it was determined for all time that I should beat you, and he continued to do so. 2 This link to fatalism followed through to early Christian theology. The idea of the Fates was supplanted by an equally powerful Christian God. In both cases a powerful entity had control and infinite knowledge into a person s determined future. 3 b. Causation Post-Enlightenment developments in science and philosophy brought us more sophisticated accounts of determinism. Causation became another more sophisticated concept tangled with determinism. This entanglement is derived from William James 1884 lecture at Harvard s Divinity School. James declared that determinism is true when the fixed parts of the world appoint and decree what the future parts will be. James continues to claim that, if determinism is true the part we call the present is compatible with only one totality. Any future complement than the one fixed from eternity is impossible. The whole is in each and every part, 2 Salmon (1998) p.2. 3 Salmon (1998) p.3-4. 5
and welds it with the rest into an absolute unity, an iron block 4 Causation creeps into the Jamesian notion of determinism. On a basic level Jamesian determinism seems to imply that every event has a cause, since the future state of the world must be appointed and decreed by the present state of the world, to be the way that it is. 5 This conception of determinism links events in a determined chain of causality. The world can be thought of as a chain of dominos once one falls they all continue to fall in a set pattern thereafter. Another important aspect of Jamesian determinism is the idea of unity. This idea of unity holds that, a difference at any time requires a difference at every time. 6 From the Jamesian picture of determinism we seem to get the view of a deterministic universe as a unified mechanistic chain of causal events. This vision, though seemingly intuitive, runs into several major problems. The first major problem is that the existence of causal chain does not guarantee against hidden possibilities. Just because every event has a cause it does not imply that the outcome of the antecedent event will always lead to one unique result. We can image the future world being caused by a present world but this does not mean that it was the only way it could have been caused by the present world. There could have been numerous indeterministic possibilities for that world to turn out. Another way to think about this problem is that if we were to run multiple trials of this world unfolding we could have numerous different future worlds from the same present world. Causation is not a strong enough concept to ground a future based determinism. Another problem is that causation is a famously controversial and vague concept. 7 Notions of causality and events are so vague in fact that they are not even used in physical theories and scientific practice. So to use these terms to explain another equally vague concept is an utterly hopeless endeavor. 4 Earman (1986) p. 5 5 Ibid. p. 6 6 Ibid. 7 Ibid. 6
c. Predictability Once the dust clears from the old notions of determinism the search continues for a conceptual meaning. The next major notion often used when in discussions of determinism is predictability. Predictability is introduced into conceptual formulations of determinism by Pierre Simon Laplace. Laplace s definition of determinism equates determinism with predictability by introducing his famous demon. We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow. An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes. 8 This definition forms the basis of theoretical determinism with ramifications for math, physics and philosophy. Laplacean determinism has a very strong intuitive backing behind it, so intuitive that it seems to form the foundations for our quest for scientific knowledge. Essentially, Laplace states that if a system is deterministic then it must work in accordance with strict laws and absolute regularity. We can conceive of a deterministic system like the inside of a watch. On Laplace s account if an all knowing intelligent being can observe the clock at time t1 and is able to tell the totality of the gear s movements, then the system is deterministic. Mark Stone teases 8 Earman (1986) p.7 7
out three requirements of Lapalcean determinism. These three requirements relate to: (1) algorithms, (2) unique evolution and (3) error. 9 If we conceive of a deterministic system that is predicable then there must be an algorithm relating the information from the present state to the result of the prediction. As Stone states, prediction is what enables us to determine an unknown state from a known state, and we do this by applying the known state as an input to a predictive algorithm. 10 The next requirement of Laplacean determinism is what has come to be called unique evolution. Unique evolution is the idea that one unique state always leads to one unique outcome. If the conditions are kept constant then a state should always produce the same outcome. We can conceptualize this by thinking of, as Robert Bishop does, a movie. 11 If you watch a film in totality then restart the film, a film following unique evolution will play back every scene in the same exact way assuming all conditions remind the same. A film set up that would spontaneously spit out sequences of film would not follow the rule of unique evolution and would not be deterministic. 12 The final constraint is that a deterministic system can be described with a relatively small non-zero error. The prediction must be precise enough to be considered errorless. 13 Laplacean determinism has come under attack for its strong link between determinism and predictability. There are two major strands of attacks on the predictability and determinism link. One is full out conceptual assault that seeks to separate the two concepts, while the other is critique of the overall notion of the demon/predictor. The first critique is represented by Mark Stone s argumentation in Chaos, Prediction and Laplacean Determinism. Stone, after laying 9 Stone (1989) p.125. 10 Ibid. p.126 11 Bishop (2005) p.3. 12 Ibid. 13 It will be error less for the demon since our measurements as humans contain some error there will always be some small error involved in our prediction. 8
down the three criteria for Laplacean determinism, seeks to wedge a divide between the two concepts. He first attacks the idea that algorithms are predictive. Stones ask us to imagine an algorithm to predict the Nth decimal place in π. The problem for this prediction is that the algorithm would have to be an open-formed solution, which means, that all digits up to the predicted digit would have to be examined to get the answer. Stone contends that after this process we have arrived at a solution where we have not predicted the value at the Nth place but rather inspected π. The algorithm we have used has not led itself to a prediction. 14 Stone also argues that deterministic chaos creates a problem for Laplacean determinism. In Stone s deterministically chaotic system changes in state are still regulated by an algorithm and this algorithm is closed. Stone contends that we will be able to make an approximation for the output of the system but it would be fraught with error. This leads to an additional requirement for Laplacean determinism. Laplacean deterministic systems must deliver accuracy in the output. According to scientific theories on chaos even if scientist could discover the controlling openform algorithm for the system, the system would work faster than the prediction; thus, for Stone, making the prediction not a prediction at all. 15 Another feature of chaotic systems is that they are error amplifying. Since we always have error, deterministically chaotic systems will always amplify error thus rendering the demand for accuracy null. 16 The lesson from the trip into deterministically chaotic systems is that there are conceivable systems that are deterministic yet that do not lead to the absolute predictability that Laplacean determinism demands. The bond has been severed. Earman launches a criticism from another direction. Earman s project is to search for an ontological understanding of determinism. In this sense, the idea of a predictor introduces an 14 Stone (1989) 125-126 15 Ibid. 126 16 Ibid. 127 9
unacceptable epistemological element into what should be an ontological discussion. He argues that the determinism that you will get from pure Laplacean understandings of determinism depends on the powers of prediction that the demon has. If the demon is all knowing then we get a strong determinism yet if the demon is like us and falls far from omnipotence then we have a much weaker determinism. This leaves us in a situation where we get no real sense of what determinism or a deterministic world actually is. There is a need to rid Laplace s and future definitions of determinism of the demon that lurks within. Earman moves forward to try to create determinism without predictability as an essential component. II. EARMAN S DETERMINISM Though Bertrand Russell makes progress in riding determinism of Laplace s demon by using a functional account of what it means for a system to be deterministic, Earman provides an account of determinism using a possible worlds schematic. 17 Earman s reformulation requires there to exist some set of worlds with a particular structure. A world for the purposes of the reformulation is a 4 dimensional space-time world. One of these is the actual world; the actual world is a world that is the collection of all events that occurred, are occurring and that will occur, where events are characterized as changes in spatio-temporal magnitudes. The rest of the 17 Bertrand Russell provides the final definition of determinism that influences Earman s reformulation. Russell notion of determinism is important for Earman because it purges the epistemological demon from Laplacean determinism. In Russell s determinism the state of a system can be represented by a function E t = f (e 1,t 1,e 2,t 2,,e n,t n ). where e are data from the system, t are times and E t represents the state of a system at a time. A deterministic system is characterized by this functional relation and if t is a time within the function then the system is deterministic. 17 The problem for Rusell s notion is that it it is trivially true. Russell himself sees this problem when he states, the whole state of the material universe at time t must be capable of being exhibited as a function of t. Hence our universe will be deterministic but if this is true no information is conveyed about the universe. In fact Earman could adopt a Russell function to describe determinism but he instead chooses to use possible worlds terminology. 10
worlds are merely possible worlds. A merely possible world on this account is a world with alternative histories to the actual world. With these components in hand we are ready to investigate Earman s definition. Letting W stand for the collection of all physically possible worlds, that is, possible worlds which satisfy the natural laws obtaining in the actual world, we can define the Laplacian variety of determinism as follows. The world W W is Laplacian deterministic just in case for any W W, if W and W agree at any time, then they agree for all times..this concept determinism can be broken down into two sub concepts. A world W W is futuristically (respectively, historically) Laplacian deterministic just in case for any W W, if W and W agree at any time, then they agree for all the latter (respectively, earlier) times. 18 Earman s determinism is essentially a supervenience statement. A system is deterministic if a certain state of the system fixes the past and future states of the system. In other words the future and past states supervene on the present state. Supervenience determinism severely limits the modal possibilities in a way that causation does not. When two things supervene on each other they are necessarily linked. So if the future state of the world W supervened on the present state of the world W it must always do so. If I were to do other trials of the world s unfolding these two specific states of the world must unfold together. Here we see the continued importance of unique evolution to both Laplacean and Earman s determinism. If the world W and its identical copy W are isomorphic in respect to their properties and have the same laws then they will have 18 Earman (1986) p.13 11
the same unique evolution. 19 Earman s definition is meant to be the continuation of a purely ontological Laplacean definition of determinism with none of Laplace s epistemology. Implicit in Earman s formulation of determinism is a distinction between transitions and properties. This distinction is made clear by Earman s declaration that determinism is not be all or nothing. What he means by this is that some of the world s magnitudes can be indeterminate, thus meaning that a world can be partially deterministic with respect to those magnitudes. 20 The properties of worlds can be indeterminate but the transitions between states of worlds must be deterministic if these states of the world supervene on one and other. Earman s definition can allow us to make metaphysical statements about determinism that the original Laplacean version cannot do without appeal to an epistemological force. While Earman s determinism forms the basis of how I conceptually use determinism in the subsequent chapters I will not focus on all of his account. Specifically my use of determinism will be limited to Earman s determinism futuristic Laplacean determinism and more specifically its upshot, unique evolution. In Earman s determinism there seems to be the assumption that the laws of nature and time work symmetrically. If one thing is fixed in the present it fixes the past and the future. In looking at the compatibility of chance and determinism we seem focused on the future with the, perhaps wrong, assumption the past is fixed. We are looking to see if there is a real chance that an object will Φ in a future time. The forward nature of chances makes it especially important to look at determinism in a manner more akin to the futuristic Lacplacean model with special emphasis on the constraint of unique evolution. 19 Bishop (2005) p. 3 20 Earman (1986) p. 14 12
III. DETERMINISM IN OUR PHYSICAL WORLD With a strong Laplacean ontological determinism intact we can now figure out whether our world is in fact deterministic. But how exactly can we do this? Assessing whether the world is deterministic will depend on our best physical theories. This, of course, assumes some sort of scientific realism about those theories. In the following section I will assess two of the paradigm physical theories. One of these theories is thought to be thoroughly deterministic while the other is thought to be thoroughly indeterministic. Though I will not delve too deeply in these theories, it is important to see that our world could be either partially or fully deterministic no matter if our world works closer to Newtonian classical mechanics or to quantum uncertainty. a. Newtonian Mechanics A world that works under the laws of classical mechanics is usually taken to be a paradigm case of determinism. A pendulum is a perfect example of case where the laws of Newtonian mechanics satisfy the unique evolution component of Laplacean determinism. Newton s gravity also seems to display the characteristics of a deterministic system. This is displayed from a mathematical standpoint. To understand how Newtonian gravitation could satisfy ontological determinism we must simplify the world into point particles with constant positive masses. Newton s second law states that the net force acting on a particle is equal to the product of the mass of the particle and its acceleration. This of course needs a further supplement to describe the nature of force. This is where Newton s law of universal gravitation arrives. This law can be famously described by the equation. This law essentially states that every point particle attracts another point particle with a force directed along a line which is proportional to the 13
product of their masses and inversely proportional to the square of the distance between the point masses. 21 If we check for the acceleration of the particle at a certain t and then verify that it its acceleration with the mass equals the gravitational force then we should get one unique mathematical answer. From discussions of Newtonian gravitation and pendulums it seems natural to view classical mechanics as necessarily deterministic but there are some serious flaws in this line of thinking. Earman contends that our notion of the determinism of Newtonian mechanics rests on a particular conception of space, time and motion. He argues that Laplacean determinism makes it the case that space cannot be both absolute and that all motion is relative to the relative motion of bodies. Since relative motions imply only relative quantities and not absolute quantities like motion there is a certain space-time to support relative motion. This space-time include three things: (1) planes of absolute simultaneity, (2) a metric to measure the spatial distance between simultaneous events and (3) a time metric. Absolute space in this space-time ultimately leads to different future positions for particles in space thus making the system indeterministic because it cannot hold relative motions. 22 Bishop states the problem for determinism and Newtonian mechanics in the following way. The root problem can be traced back to the fact that one s mathematical theorems only guarantee existence and uniqueness locally in time. So he concludes that determinism might hold locally, but this does not guarantee determinism must hold globally. 23 Newtonian mechanics must not be completely deterministic. From these discussions it is obvious that classical mechanics is not as deterministic as it seems, furthermore it seems that of notions of 21 Earman and Butterfield (2007) p. 234-235 22 Earman (2004) p.2-3 23 Bishop (2005) p.4-5 14
space, time and motion may make Newtonian mechanics, the paradigm of determinism, not be deterministic at all. b. Quantum Mechanics Now that we can see that classical mechanics is not as deterministic as it is thought to be we must look at quantum mechanics under the light of determinism. Quantum mechanics, contrary to classical mechanics is thought of as a paradigm case of indeterminism. This perspective is seen in Einstein s famous quote, God doesn t play dice. This quote originated as a curt response to Max Born and Schrodinger and Heisenberg s new field of quantum theory. Quantum theory is often thought of as indeterministic with regards to the particles that make up a wave. Particles that make up waves are thought to be indeterministic in terms of measuring individual particles evolution. Not only are these particles able to be measured in practices they cannot be measured in principle. But there are theories like the Pilot-Wave theory which state that a wave evolves deterministically over time thus determining the motion of the particles of the wave, so that the particles follow a unique evolution. This theory is compatible with quantum systems and determinism. 24 What the Pilot-Wave theory does is allow for a phenomenon that is thought of as indeterministic and in the realm of quantum theory and proving a plausible way in which it could still be deterministic and follow the laws of quantum mechanics. Again we see that quantum mechanics may not be as indeterministic as it seems. The lesson to take from our insight into classical and quantum mechanics is that the best theories of the physical world are indeterminate as whether they are deterministic. Classical mechanics is supposed to be the shining example of a deterministic theory yet, as Earman shows, 24 Bishop (2005) p.5-6 15
this need not necessarily be the case. On the other hand the credentials of quantum mechanics, the paradigm of indeterminism, are called into question by theories like Pilot Wave theory which show a way in which determinism and quantum mechanics are compatible. The point of this discussion was not to provide a definitive answer to the compatibility of determinism and these physical theories. These topics are extremely complex and could warrant a complete thesis in their own right. What I hoped to do was show that the mechanisms (for which ever physical theory) of our world are a lot more complex then they seem at first. Our world despite which ever theory may be true may show elements of determinism and indeterminism. CONCLUSION In this chapter we have climbed up the Tower of Babel to arrive at a working definition of determinism. I have settled on Earman s reformulation of Laplacean determinism, not because it is without errors, but because it is the best available option. Earman s definition removes epistemological notions and confused and controversial elements of causation. This leaves an ontological determinism that is robust enough to investigate ontological questions about chance. It should be noted that from here on that the notion of determinism used in this thesis will refer to Earman s reformulation with special emphasis on unique evolution. From determinism I dived into the world of physics. In trying to figure out the true indeterministic/deterministic character of our universe I showed that our best theories provide little conclusive results. This sets the stage for the question that will be the focus of the rest of the thesis. From the inconclusiveness of the scientific theories we can conclude that our world could very well be deterministic, or partially deterministic. We can also definitely say that deterministic universes are a possibility and that other possible universes might be deterministic even if this one is not. Knowing that 16
determinism is a valid possibility we can now turn our sights on investigating the metaphysical ramifications of deterministic systems on objective chance. 17
CHAPTER II AN UNHOLY UNION? Thus there cannot be deterministic chance. All there can be is deterministic ignorance. (Schaffer 2007) INTRODUCTION Our best physical theories of the universe have proved inconclusive on the veracity of determinism. No matter which physical theory happens to be true, be it closer to classical mechanics or quantum theory, there appears to be at least a possibility of determinism. Moreover, even if our world is not deterministic it seems that determinism could be true in some other possible world. It is with these possibilities that we must consider the metaphysical ramifications of determinism. The specific ramification that I will be investigating is the ramifications of determinism on chance. Are determinism and chance compatible? What would it be to have a concept of chance that was compatible with determinism? In the current chapter I will address these questions. I will investigate the contours of chance, what a deterministic chance could be and arguments for their incompatibility. Although this chapter will end on a pessimistic note by echoing Jonathan Schaffer in claiming that the major compabilitist theories of deterministic chance fail in the following chapter I will pursue a more positive account of deterministic chance. I. THE PROBLEM It is the start of a football game and both teams come to the 50 yard line. At the 50 yard line a referee presents a fair sided coin with a side marked heads and a side marked tails. The referee asks one team to choose one side while the coin is flipping in the air. If the coin lands on the side that the team selected then that team gets the privilege of choosing how to start the game. This is an example of a coin flip. The intuition behind the coin flip is that a fair coin has 2 sides and that both of these sides are equally weighted, and that therefore there is a 50% chance that 18
either side is landed on. The simplicity of this case has made the coin flip a paradigm case of chance. But there is a deeper intuition that grounds the coin flip. When we flip the coin we believe that there is an almost undeterrmined future for the coin, meaning that there is an actual ability for the coin to flip either heads or flip tails. After the coin flip we think that it actually flipped that it could have flipped otherwise. This chance is what is referred to as objective chance. Objective chances are not restricted to coin flips- they also seem to play a vital play in science. One of the most prominent examples of objective chances in the deterministic chance literature is radioactive decay. Radioactive decay is seemingly based on objective chances and objective probability. Particular samples of radioisotopes are unstable and unpredictable. Scientists try to get a sense of the half-life of the isotope by assuming that these events are completely random. From this scientists observe patterns of decay by taking into account the chances and randomness of the behavior of the nucleus. In this case objective chance has an explanatory role in science. There are other examples of probabilistic laws in science but those will be looked at in greater detail in the following sections. That seems simple. It seems to be an open and shut case- our world consists of objective genuine chances. This is the strong intuition that we act on and live our lives by but this like so many of our intuitions calls for stronger investigation. Let us turn back to our work on determinism. We roughly arrived at the concept of determinism as something like this the world in its current state supervenes on the world at a past time. This introduces us to the idea of unique evolution. If a system is to have a certain set of initial conditions then it will result in a unique outcome. So what does this mean for chance? It seems as though the progression of the world and its laws must already dictate an outcome of a chancy event(an event with an objective 19
chance between 0 and 1) if determinism is true, thus meaning that determinism and chance are incompatible. This is similar to the seeming incompatibilism of determinism and libertarian notions of free will. If determinism is true it seems the coin that we are flipping could not have flipped any other way than what it actually flipped. If the coin is placed into intial conditions of the same sort than it should always produce the same one outcome. But this defines everything we have learned about probability. We know that the chance of a coin flipping heads or tails is 0.5 but if determinism is true than it must be 1 (it will occur) or 0 (it will not occur). In a deterministic world it seems like there cannot be chances between 1 and 0. What are we to make of this conundrum? There are two ways in which this problem can be solved. The first way is to declare the two concepts incompatible and to either argue there are no objective chances or argue determinism is false. The other option is to take the compatibilist track and argue for a deterministic conception of chance. The choice taken by incompatibilist is to claim that there are no objective chances and claim that the chances that we think come up between 0 and 1 are actually epistemic chances. Epistemic chances are merely our guesses of the likelihood of a future event. We do not know all of the deterministic laws of nature therefore we guess the outcome of the coin flip even though it is metaphysically decided. Epistemic chances comes from our ignorance. There is no open undetermined future and thus no genuine way the object could do otherwise. The epistemic or subjective chances have come under fire from a cadre of compabilist philosophers trying to craft room for an objective notion of chance. Before we dive into the compabilist accounts of chance we must have a deeper metaphysical understanding of the role we need an objective chance to fill. II. THE ROLE OF CHANCE 20
The incompatibilist position is strong and may characterize most philosophers feelings on the issue but it has not squashed the incompatibilist s project. A few philosophers have tried to provide an account of deterministic chance. In order to understand how a determinsitc chance works we need a deeper metaphysical understanding of chance. In order to analyze chance I will be borrowing a critical distinction Jonathan Schaffer develops in his aptly titled essay Deterministic Chance. Schaffer makes the distinction between chance-formal and chancesubstantive. A. CHANCE-FORMAL A concept of objective chance is linked with an account of objective probability. Schaffer explicates a formalistic definition of chance which takes on a probabilistic character. He calls this account chance-formal because it is a based line definition with little metaphysical import. Chance formal includes three major parts: p, t and w where p represents the proposition that the event occurs w represents a world and t represents the time in which the event is occurring. Put together with chance we get ch<p,w,t> which reads the chance of p holding at world w and at time t. The chance function also must have a component that explains that represents and that in our world there are chances between 0 to 1 that proposition p will hold. This leaves us with our formalistic account of chance: Chance is probability function: ch<p,w,t,> [0,1]. 25 The interval in the function is to be read as between 0 and 1. So put in terms of a coin flip: ch<p head, w, t> [0.5]. This provides a formal representation of our basic understandings and intuitions of what a chance is. The problem with chance-formal is that by itself it does not 25 Schaffer (2007) p.115. 21
distinguish between epistemic and objective chances. A chance from that function could be between 0 and 1 yet be epistemic. What is necessary is more metaphysical meat on the strong formal skeleton. B. CHANCE-SUBSTANTIVE Schaffer provides a list of six generally accepted metaphysical notions to which chance is connected. The six notions are: the principle principal, the basic chance principle, the realization principle, the future principle, the intrinsicness requirement, the lawful magnitude principle and the causal transition constraint. The combination of these notions creates what Schaffer calls chance substantive. Chance substantive can give us a greater understanding of the metaphysical relationship between theories of objective chance and determinism. 26 The first and most discussed of these requirements is David Lewis Principal Principle. Lewis Principal Principle (PP) was first introduced in his A Subjectivist s Guide to Objective Chance (SGOC) in 1986. The Principal Principle basically connects our epistemic belief in a chance occurring to the metaphysical chance occurring. Lewis begins SGOC begins by parsing notions of probability from chance. As a subjectivist about probability Lewis sees probability as nothing more an epistemological framework but he is trying to craft a space for objective chances. Subjective probability involves both credence and objective chances for Lewis. Credence is a rational belief in the outcome of an event. Lewis classes credence and chance as filling two different concepts of probability. He seeks to investigate the second-order relationship between these two concepts of probability, and more specifically credence about 26 Ibid. p. 123. 22
chance. Credence about chance involves the rational belief in the chance of an event occurring. The relationship between the notions is what creates the Principal Principle. Lewis believes that the Principal Principle encompasses all that we need to know about chance. He develops the principle through a four part questionnaire. The questionnaire is supposed to show the linkage of rational belief in the proposition about an event and the chance of the event happening. If a fair coin if flipped then there is a 50% chance that the coin will land heads but it also must be true that our belief in the coin flipping heads must also be 50% due to your knowledge that the coin is fair. The questionnaire also shows the importance of evidence in forming a rational belief. 27 This leads to the Principal Principle. The Principal Principle has five major components: the credence function, a real number x, the proposition X and admissible evidence E. The credence function is a probability distribution over (at least) the space whose points are possible worlds and whose regions (sets of worlds) are propositions. 28 The next portion is x where x is a real number. This real number is the chance of an event occuring at a certain time. The Proposition X is the proposition that the chance, at time t, of A s holding equals x. 29 What is admissible is represented by E. Lewis allows two pieces of information to be admissible: 1) historical information up to the time of the event and 2) hypothetical information about the chance itself are admissible. What is not admissible is the actual occurrence of the event. With these parts in hand the Principal Principle can be stated: Principal Principle: C(A/XE)=x 30 The credence in A holding with the admissible evidence will equal the chance of the event occurring. Though Lewis may have thought this was this was exhaustive of chance, there seems like there are many more metaphysical components of chance. 27 Lewis (1986) p.265. 28 Ibid. p.266. 29 Ibid. p.269. 30 Schaffer (2007) p. 23 23
The next principle Schaffer borrows from Bigelow et. al. The borrowed principle is the Basic Chance Principle. The Basic Chance Principle, as stated by Bigelow et. al, is the idea that if we suppose x>0 and Ch tw (A)=x. Then A is true in at least one of those worlds w that matches w up to time t and for which Ch t (A)=x. The Basic Chance Principle states that if there is a non-zero chance that an event occurs at t in w then there is some possible grounding world where the event occurs which also matches the world w s history up to time t. Since the possible world grounds the present world and they are the same until t, the chances on both worlds are the same. Written in a Schaffer s framework the Basic Chance Principle reads as this: Basic Chance Principle: If ch<p,w,t>>0, then there exists a world w ground such that: (i) p is true at w ground, (ii) w ground matches w in occurent history up to t, (iii) ch<p, w ground, t> = ch<p,w,t>. 31 The Realization Principle is very similar to the Basic Chance Principle. The only difference is that the Realization principle adds the requirement that the grounding world and the actual world match with respect to laws. The justification for this principle is straightforward. The laws of the universe fix the chance of an event occurring in the actual world so the same laws must be in place to ground the chance in the possible world. The fourth principle involves the future. David Lewis explains how chances in the world are time-dependent. 32 Lewis uses the example of reaching the end of a maze to explain the timedependent nature of chance but I will use a rather morbid example to draw out this intuition. Joe was in a terrible accident and has been flown to the emergency room. If doctors cannot save life in an hour he will die. At the time of arrival, 11:00 PM there is a 50% chance that the doctors will be able to save Joe by 12:00 AM. Its 11:30 PM and still no success by the doctors; Joe s chance of survival has decreased to 25%. At 11:50 PM when Joe s chances are at a mere 10% 31 Ibid. 24 32 Lewis (1986) p. 271 24
the doctors fortuitously manage to perform the necessary operation for Joe s survival. At 11:55 the operation is done and Joe s chance of survival is 100%. This example and Lewis labyrinth example are supposed to show that chance not only has a time dependent element but also that chance concerns elements in the future. Chance exploits the asymmetrical nature of time. This aspect of chance informs the future principle: 33 Future Principle: If 0 <ch<p e,w,t> <1, then t<t e The principle reads that if the chance of an event occurring is between 0 and 1 then the time of the event must be in the future. The Intrinsicness Requirement is relatively simple. If an intrinsically duplicate is put through the same test under the same conditions then the chance of the duplicate Φ-ing will be the same in all duplicate trials. 34 If I had three coins and two of these coins were intrinsic duplicates and the coins were flipped in intrinsically duplicate trials then the chance of the coins flipping heads should all be the same value. 35 The Lawful Magnitude Principle is supposed to connect chances to laws. Schaffer states that the Lawful Magnitude Principle is: If P tw (A)=x, then there is a lawfully entailed history-to-chance conditional of the form: if the history through t is H, then ch tw (A)=x. 36 The LMP is supposed to show the close relationship between the laws of nature, through historyto-chance conditionals, and the specific chance values. Where the BCP and the RP relate chance to worlds the LMP shows how chances work in relationship to laws. 33 Schaffer (2007) p.125. 34 Intrinsic duplicates are the same in every property of the object that makes up an essential part of what it means to be that object. 35 Schaffer (2007) p.125-126 36 Ibid. p. 126. 25
The last requirement of chance-substantive deals with causation. Arguments for objective chance often leave a place for chances to explain various causes and effects. Adherents to objective chances used radioactive decay and events like ice melting to appeal to this argument. But in order for this to be true the chance must be within the transition. Outside of the transition the chance has no impact. Schaffer calls this the Chance Transition Constraint. Casual Transition Constraint: If ch<p e, w, t> plays a role in the causal relation between c and d, then t e ϵ[tc, td]. 37 With these principles complete Schaffer s chance-substantive. In conjunction with chance-formal we have a complete definition of what an objective chance must be. Chance: Chance is the probability function from propositions, worlds, and times onto the closed unit interval, which best satisfies: (i) the Principal Principle, (ii) the Realization Principle, (iii) the Futurity Principle, (iv) the Intrinsicness Requirement (v) the Lawful Magnitude Principle and the Causal Transition Constrain. 38 A complete conceptual understanding offers much more than mere clarity. The new understanding of chance with these formal and substantive elements allows the theories of chance to be adjudicated. C. TYPES OF CHANCE Beyond a conceptual understanding of chance Schaffer also explains the various types of deterministic chances that have been argued for. In the philosophical literature there is a tradition 37 Ibid. 38 Schaffer (2007) p. 126. 26